Systematically.
#1 Where you go to medical school matters for residency placement. Anyone that tells you otherwise doesn't know anything about residency or is lying to you. I'm sorry, but your father doesn't know what he is talking about. First, there is a gap between US MD schools and US DO schools and then a substantially larger gap between those two and everything else. You will be at a huge disadvantage coming out of the Caribbean. For every success story, there are 10, if not more unhappy stories and probably 10 more disaster stories. What people will debate is, how much difference between different US MD schools there is. For the vast majority of applicants (90%+) the US MD schools are functional equivalents. However, if you are looking at going into a competitive specialty or a competitive academic program in any specialty, what school you go to matters.
#2 Where you go to medical school matters for your education. Your first two years of school are going to be basic science and organ system classroom learning. There is very little difference between different schools. Some would even make the argument that a well organized, motivated student could self study the first two years and turn out just as well as any US MD student. What is different between schools and where there is a huge difference between US MD schools and everything else is the quality of rotation sites. If you are at Hopkins, you rotate at only Hopkins hospitals, unless you choose to do some electives elsewhere. And yes, where you do your clinical rotations matter. Can you still learn and do well not going to a big name program, yes. But, you are going to be at a disadvantage later.
#3
https://www.aamc.org/download/321518/data/factstable25-4.pdf
If you take all 3600 Caucasian students that had a 3.60-3.79 PGA and a 27-29 MCAT, 45% of them got into a US MD school. DO NOT MISINTERPRET this statistic. This does NOT mean that you have a 45% chance of getting into medical school. It means that a good number of people with your statistics will get into medical school somewhere. The ones that do, a) applied smart and broad, b) had other things on their applications that made them superior to the others in the applicant pool. It is well worth taking a full year to apply once and apply well. With good planning and some buffing, you stand a reasonable shot at getting into a US MD program. Forget the minors/double majors. They are meaningless. If you prepared inadequately for the MCAT the first time, you should evaluate if you can reasonably improve on your score. You should retake if in your estimation you can on average improve your score by 3 or more points. Then you should focus on continuing your ECs and developing stronger connections for your letters.